During its first three years, the Tropical Rainfall Measuring Mission (TRMM) satellite observed nearly six million precipitation features. The population of precipitation features is sorted by lightning flash rate, minimum brightness temperature, maximum radar reflectivity, areal extent, and volumetric rainfall. For each of these characteristics, essentially describing the convective intensity or the size of the features, the population is broken into categories consisting of the top 0.001%, top 0.01%, top 0.1%, top 1%, top 2.4%, and remaining 97.6%. The set of 'weakest / smallest' features comprises 97.6% of the population because that fraction does not have detected lightning, with a minimum detectable flash rate 0.7 fl/min. The greatest observed flash rate is 1351 fl/min; the lowest brightness temperatures are 42 K (85-GHz) and 69 K (37- GHz). The largest precipitation feature covers 335,000 sq km and the greatest rainfall from an individual precipitation feature exceeds 2 x 10(exp 12) kg of water. There is considerable overlap between the greatest storms according to different measures of convective intensity. The largest storms are mostly independent of the most intense storms. The set of storms producing the most rainfall is a convolution of the largest and the most intense storms. This analysis is a composite of the global tropics and subtropics. Significant variability is known to exist between locations, seasons, and meteorological regimes. Such variability will be examined in Part II. In Part I, only a crude land / Ocean separation is made. The known differences in bulk lightning flash rates over land and Ocean result from at least two differences in the precipitation feature population: the frequency of occurrence of intense storms, and the magnitude of those intense storms that do occur. Even when restricted to storms with the same brightness temperature, same size, or same radar reflectivity aloft, the storms over water are considerably less likely to produce lightning than are comparable storms over land.